Scalar Dark Matter with a $\mu\tau$ Flavored Mediator

We study a renormalizable scalar singlet dark matter model based on $Z_4$ lepton flavor symmetry. A $\mu\tau$-philic scalar doublet is introduced to explain the discrepancy between the experimental value and the theoretical prediction of the muon anomalous magnetic moment. At the same time, these flavored scalars play the role of a mediator which connects dark matter and standard model particles. The observed relic abundance of the dark matter is easily maintained while satisfying the current severe constraints on the dark matter from various experiments and observations thanks to the flavor off-diagonal interactions of scalar mediators. We also explore the possibility of dark matter direct detection through the one-loop process.